← etc / Encyclopedia of Triangle Centers

X₉₂₆¶

CROSSDIFFERENCE OF X₆ AND X₇

As the isogonal conjugate of a point on the circumcircle, X₉₂₆ lies on the line at infinity.

X₉₂₆ (CROSSDIFFERENCE OF X₆ AND X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_926 = CROSSDIFFERENCE OF X_6 AND X_7."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00926(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_926 = CROSSDIFFERENCE OF X_6 AND X_7 on reference triangle ABC."""
            X_926 = eval_trilinear_point(model, A, B, C, 'a*(a - b - c)*(b - c)*(a*b + a*c - b**(2) - c**(2))', ID="X_926", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_654 = eval_trilinear_point(model, A, B, C, 'cos(A - B) - cos(C - A)', ID="X_654", classes=["center", "incident"])
            central_line(model, X_55, X_654, 55, 654, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_692 = eval_trilinear_point(model, A, B, C, 'a**(2)/(b - c)', ID="X_692", classes=["center", "incident"])
            central_line(model, X_101, X_692, 101, 692, incident=True)
            return promote_point_to_top(model, X_926)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_926 on the given reference triangle."""
            model = create_model('X_926 = CROSSDIFFERENCE OF X_6 AND X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00926(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-00926.json"))
            write_center_svg(
                model_acute,
                here / "x-00926.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X926¶

X₉₂₆¶